Intensity mapping of the H I 21 cm line and the CO 2.61 mm line from the epoch of reionization has emerged as powerful, complementary, probes of the high-redshift Universe. However, both maps and their cross-correlation are dominated by foregrounds. We propose a new analysis by which the signal is unbiased by foregrounds, i.e. it can be measured without foreground mitigation. We construct the antisymmetric part of two-point cross-correlation between intensity maps of the H I 21 cm line and the CO 2.61 mm line, arising because the statistical fluctuations of two fields have different evolution in time. We show that the sign of this new signal can distinguish model-independently whether inside-out reionization happens during some interval of time. More importantly, within the framework of the excursion set model of reionization, we demonstrate that the slope of the dipole of H I-CO cross-power spectrum at large scales is linear to the rate of change of global neutral fraction of hydrogen in a manner independent of reionization parameters, until the slope levels out near the end of reionization, but this trend might possibly depend on the framework of reionization modelling. The H I-CO dipole may be a smoking-gun probe for the speed of reionization, or standard speedometer for cosmic reionization. Observations of this new signal will unveil the global reionization history from the midpoint to near the completion of reionization.
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